After you via a registrar have applied for a domain name during Sunrise you will get an email asking you to send in documentary evidence proving your prior right for the domain name you are applying for. The deadline for doing this is 40 days. If you, for some reason, don't get an email after your applicatons is sent in, please check with your registrar.
Some times a third party is offering the service of dealing with this paperwork. If you have agreed so the email mentioned above is sent directly to that address instead.
In the WHOIS database (www.whois.eu) you can see what the deadline is for when your documentary evidence need to be recieved, when it is received or if the deadline has expired. In the WHOIS you can also see if anyone else has applied for the same domain name.
If no documentary evidence is received within 40 days the application expires and an email is sent to the applicant explaining this.
If the deadline for sending in documentary evidence expires, or your Sunrise application is rejected, it is possible to apply again, and then correct whatever mistake that caused the rejection.
If everything is in order and your application is accepted there will be a 40 days period before you can start using your new domain name. During this time it is possible for someone, who may think that the procedure of attributing the domain name was wrong, to file a complaint via the ADR process (Alternative Dispute Resolution.)